Mash together butter, miso and lime zest in a bowl until smooth and combined.
Use a shucking knife to open the oysters, prying them open at the hinge and discarding top shell. Leave oyster attached to bottom shell. Place oyster halves on a sheet pan and dollop about a teaspoon of miso butter in the shell. Sprinkle with breadcrumbs and season with freshly ground black pepper.
Using tongs, carefully place oysters on the grill over direct heat, make sure they are flat so butter doesn’t spill out.
Cook until oyster begins to shrivel and butter bubbles a bit, 4- 8 minutes depending on the size of the oyster and thickness of the shell. Transfer to a heatproof platter. Serve with lime wedges and crusty bread, for dipping in the sauce leftover in the shell.